ECE News Story

Course Description: Classical coding theory (which was founded almost 50 years ago) studies codes from theiralgebraic viewpoint. It served communication theorists and practitioners well, but essentiallyfailed to reach the goal set by information theory, i.e., to provide codes that come close tochannel capacity. However, 15 years ago, channel coding theory was revolutionized by theinvention of turbo codes and the re-invention of low-density parity-check codes. This revolution led to the birth of the new subfield of modern coding theory.

In the first part of the course, we will review some basic results from information andcoding theory (e.g., error exponents) in order to see what is the best one should expect froma good code. In the second part, we will study families of good codes, collectively referred toas turbo-like codes. Their asymptotic and finite-length performance, and their encoding anddecoding complexity will be studied. This investigation will conclude by looking at familiesof codes that provably approach the capacity of the binary erasure channel and we will askthe question of whether everything that Shannon predicted has been achieved.

The third part of the course deals with the multi-antenna wireless fading channel, whichpromises bandwidth efficiencies on the order of tens of bits per second per Hertz. Its capacitywill be investigated and families of space-time codes will be introduced and analyzed.

In the last part of this course a few topics in modern coding theory that have the potentialto drive the state of the art in the next twenty years will be presented. Such topics includechannel coding with transmitter side information, coding in the presence of feedback, connectionsbetween communications and control, coding for multi-user channels, recent capacityachieving codes such as polar codes, etc. [Full Story]